Chap 5. Design of Seawalls

5.1 Wave Overtopping Rate of Seawalls

Overtopping occurs if (if no parapet) chR >

Overtopping may cause flooding, erosion, wave transmission ↓ ↓ ↓

drainage protection mooring of ships 5.1.0 Overtopping Rate of Regular Waves

= discharge per unit crest length )(td

∫= mT

m

dttdT

q00 )(1 ; = duration of experiment mT

Volume = mTq0

Empirical formula (in SPM):

( )⎪⎩

⎪⎨

⎧

≤

>⎟⎟⎠

⎞⎜⎜⎝

⎛+−

=

c

cc

c

hR

hRhRhRHgqq

for 0

for '*

2/130

*0

0

α

where = unrefracted deepwater wave height '0H

*0q , = empirical constants *α

αα /1085.0* =

Estimate α , using Figs. 7-24 to 7-29 in SPM ( ) *0q *

0*0 qQ =

Usually = 1 ~ 2. *α

5.1.1 Overtopping Rate by Random Sea Waves Overtopping rate averaged over the duration of storm waves

∑=

=0

10

),(1 N

iii THQ

tq

where = duration of storm waves ∑=

=0

10

N

iiTt

0N = total number of waves ),( ii THQ = amount of overtopped water by -th individual wave i

with height and period iH iT Overtopping rate of random waves, , can be approximated by using for regular waves:

q 0q

∑=

≅0

10

0

),(1 N

iiii THqT

tq

which neglects 1) random process of wave breaking, 2) presence of surf beat, 3) interference by preceding waves. Assuming for all (= 1 to ), further approximation can be made to give 3/1TTi = i 0N

∫∞

=≅0 3/10exp )(),( dHHpTHqqq

where

),( 3/10 THq = overtopping rate by regular waves with height H and period 3/1T)(Hp = probability density function of wave height (e.g. Rayleigh distribution)

Note: Estimation of overtopping rate by assuming the random waves as a regular wave with and may give underestimated results because the estimation ignores the existence of individual waves higher than the significant wave.

3/1H 3/1T

5.1.2 Wave Overtopping Rate of Vertical Revetments and Block Mound Seawalls Vertical revetment

Dimensional analysis indicates

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛=

',

',',function

'2 000

03

0Hh

Hh

LH

Hg

q cθ

'0H = equivalent deepwater wave height corresponding to 3/1H Use Figs. 5.1 and 5.2 in the text.

For given '

,'

,',000

0

Hh

Hh

LH cθ → obtain ( )30 '2/ Hgq using the left part of the figures

→ calculate directly for given ' (or use the right part of the figures) q 0H

Block mound seawalls

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛=

',

',',function

'2 000

03

0Hh

Hh

LH

Hg

q cθ

Use Figs. 5.4 and 5.5 in the text. Note:

Given θ , , , , → : large variation (cf. Table 5.1 in text) '0H 0L h ch q

But,

Given θ , , , , → : small variation ('0H 0L h q ch %20± )

Figs. 5.1, 5.2, 5.4, and 5.5 give only order of magnitude of overtopping. Hydraulic model test is desirable for more accurate results.

5.2 Crest Elevation 5.2.1 Design Principles for Determination of Crest Elevation Run-up based design:

- Set the crest level higher than run-up height so that no overtopping will occur - No countermeasure for the case of overtopping - Impossible to build a high seawall to allow no overtopping - Possible damage in case of extraordinary storm

Overtopping-based design:

- Allow some extent of overtopping - Consider drainage system and countermeasure for erosion against overtopping - Tolerable limit of overtopping?

5.2.2 Tolerable Rate of Wave Overtopping Viewpoint of structural safety:

- Erosion of soil should be considered - Paved structure → higher tolerable limit of overtopping (See Table 5.2)

Coastal dyke Revetment

Viewpoint of utilization of land:

- Densely populated area: s/mm01.0 3 ⋅≤q- Coastal highway: s/mm10 34 ⋅≤ −q

5.2.3 Determination of Crest Elevation of a Seawall

For given , q ⎟⎟⎠

⎞⎜⎜⎝

⎛= ',,',

'function

' 00

0

00

HLH

Hh

Hhc θ : Figs. 5.6 and 5.7

- In shallow water, as , but, in deep water, the effect of bottom slope is

negligible.

↑ch ↑θ

- as , but, for the same , as and . ↑ch ↓00 /' LH 00 /' LH ↑ch ↑'0H ↑0L

- Vertical revetment versus block mound seawall

In general, , but ( ) ( )Ncc hh >0 ( ) ↑Nch as (long period waves) ↓00 /' LH

( ) ↓Nch as (wide crown width) ↑N

- Vertical revetment versus sloping seawall

More overtopping than vertical revetment ↓ Need higher crest elevation

5.3 Required Weight of Concrete Blocks

Let = characteristic length of armor unit, so that l

33 lglW ss γρ =∝

where sγ = unit weight of armor unit. Assuming the armor unit is fully submerged (worst case),

( ) 3lW wsnet γγ −∝

Express drag force 22

21 luCdwρ∝ .

Force balance at initiation of movement:

drag force + θμθ cossin netnet WW =

where μ = friction coefficient between armor units. Now

)sincos(21 22 θθμρ −∝ netdw WluC

Using )(~ gHOu ,

( ) )sincos(21 32 θθμγγρ −−∝ lHlgC wsdw

( ) )sincos( θθμγγ −−∝

ws

Hl

)sincos)(1( θθμ −−∝

rSHl ;

w

srS

γγ

=

Since , 3lW sγ∝

θγ

cot)1( 3

3

−=

rD

s

SKHW

This is the Hudson formula, where θcot is used instead of , and

= stability coefficient, which includes everything not accounted for (see Table 7.8, SPM).

3)sincos( θθμ −

DK

↑DK as number of layers ↑ and for special placement (vs random placement).